GENETIC ALGORITHMS AND GENETIC PROGRAMMING

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GENETIC ALGORITHMS AND GENETIC PROGRAMMING
Ehsan Khoddam Mohammadi
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DEFINITION OF THE GENETIC ALGORITHM (GA)
The genetic algorithm is a probabilistic search
algorithm that iteratively transforms a set
(called a population) of mathematical objects
(typically fixed-length binary character
strings), each with an associated fitness value,
into a new population of offspring objects using
the Darwinian principle of natural selection and
using operations that are patterned after
naturally occurring genetic operations, such as
crossover (sexual recombination) and mutation.
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Biological Background

• Chromosome (Genome)
• Genes
• Proteins (A T G C)
• Trait
• Allele
• Natural Selection (survival of fittest)

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GA FLOWCHART
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Which problems could be solved by GA?

• Nonlinear dynamical systems - predicting, data
  analysis
• Designing neural networks, both architecture and
  weights
• Robot trajectory
• Evolving LISP programs (genetic programming)
• Strategy planning
• Finding shape of protein molecules
• TSP and sequence scheduling
• ?All Optimization Problems (Knapsack,Graph
  coloring,)

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GA Operations

• Encodings
• Initiate Population
• Selection
• Reproduction
• Crossover (sexual reproduction)
• Mutation

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GA Operations (Cont.)ENCODING(1/3)

• Fixed-Length encoding
• 1D encoding arrays, lists, strings,
• 2D encoding matrices,graphs
• Variable-Length encoding
• Tree encoding binary parser trees like
  postfix,infix,

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GA Operations (Cont.)ENCODING (2/3)

• Permutation Encoding
• Map Coloring problem , TSP,
• Array in size of regions, each cell has an
  integer corresponding to available colors.
• R1 G2 B3 W4
• Binary Encoding
• Knapsack problem, equation solving ()
• Chromosome A 101100101100101011100101 Chromosome
  B 111111100000110000011111

1 2 2 3 1 4 4 1 2 2
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GA Operations (Cont.)ENCODING (3/3)

• Tree encoding
• Genetic programming, finding function of given
  values (elementry system identification)

( do_until  step  wall )
(  x  ( /  5  y ) )
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GA Operations (Cont.)SELECTION (1/3)

• In GA ,the object is to Maximizing or Minimizing
  fitness values of population of Chromes.
• Fitness Function should be applicable to any
  Chromes (bounded).
• Mostly a positive number, showing a distance
  between present state to goal state.
• In NP-Complete or partially defined problems
  should relatively be computed .
• Two important parameters
• Population diversity (exploring new areas)
• Selective pressure ( degree to which better
  individuals are favoured)

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GA Operations (Cont.)SELECTION (2/3)

• Roulette Wheel Selection (improved by Ranking)
• Sum Calculate sum of all chromosome fitnesses
  in population - sum S.
• Select Generate random number from interval
  (0,S) - r.
• Loop Go through the population and sum
  fitnesses from 0 - sum s. When the sum s is
  greater then r, stop and return the chromosome
  where you are
• Not suitable for highly variance populations
• Using RANK Selection
• The worst will have fitness 1, second worst 2
  etc. and the best will have fitness N (number of
  chromosomes in population).
• Converge Slowly

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2
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GA Operations (Cont.)SELECTION (3/3)

• Steady-state Selection (threshold)
• Fittest just survived
• Elitism
• Fittest selected, for others we use other
  selection manners
• Boltzmann Selection
• P(E)exp(-E/kT), like SA. Number of selections
  reduces in order of growing of age
• Tournament Selection

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F.Nitzche
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GA Operations (Cont.)REPRODUCTION(1/1)

• Reproduction rate
• Selected gene transfers directly to new
  Generation without any change.

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GA Operations (Cont.)CROSSOVER(1/1)

• CROSSOVER rate
• Single Child
• Single-Point
• 1100101111011111 11001111
• Multi-Point
• Uniform
• Arithmetic
• 11001011 11011111 11001001 (AND)
• Multi Children

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GA Operations (Cont.)MUTATION(1/1)

• Mutation rate
• Inversion
• Deletion and Regeneration
• For TSP is proved that some kind of mutation
  causes to most efficient solution

11001001 gt  10001001
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GA EXTENTIONS (part 1)

• GENETIC PROGRAMMING
• solve a problem without explicitly programming
• Writing program to compute X2X1

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GENETIC PROGRAMMING
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Genetic Programming (1/4)PREPARATORY STEPS
Objective Find a computer program with one input (independent variable X) whose output equals the given data
1 Terminal set T X, Random-Constants
2 Function set F , -, ,
3 Fitness The sum of the absolute value of the differences between the candidate programs output and the given data (computed over numerous values of the independent variable x from 1.0 to 1.0)
4 Parameters Population size M 4
5 Termination An individual emerges whose sum of absolute errors is less than 0.1
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Genetic Programming (2/4) initial population
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Genetic Programming (3/4)FITNESS OF THE 4
INDIVIDUALS IN GEN 0
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GENETIC PROGRAMMING (4/4)
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REPRESENTATIONS

• Binary decision diagrams
• Formal grammars
• Coefficients for polynomials
• Reinforcement learning tables
• Conceptual clusters
• Classifier systems

• Decision trees
• If-then production rules
• Horn clauses
• Neural nets
• Bayesian networks
• Frames
• Propositional logic

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GA EXTENTIONS (part 2)

• Multi Modal GA
• SOCIAL MODEL religion based
• Hybrid Methods ( associate with FL and ANN)

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REFRENCES

• Neural Networks, Fuzzy Logic and Genetic
  Algorithms ,Synthesis and Applications
• S.Rajasekaran
• G.A.Vijayalakshmi Pai
• PSG College of Technology,Coimbatore
• http//www.smi.stanford.edu/people/koza
• Doctor John R. Koza
• Department of Electrical Engineering
• School of Engineering
• Stanford University
• Stanford California 94305
• http//cs.felk.cvut.cz/xobitko/ga/
• Marek Obitko, obitko_at_email.cz

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